Generates a p \times p autocorrelated covariance matrix

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Description

This function generates a p \times p autocorrelated covariance matrix with autocorrelation parameter rho. The variance sigma2 is constant for each feature and defaulted to 1.

Usage

1
cov_autocorrelation(p, rho, sigma2 = 1)

Arguments

p

the size of the covariance matrix

rho

the autocorrelation parameter. Must be less than 1 in absolute value.

sigma2

the variance of each feature

Details

The autocorrelated covariance matrix is defined as: The (i,j)th entry of the autocorrelated covariance matrix is defined as: ρ^{|i - j|}.

The value of rho must be such that |ρ| < 1 to ensure that the covariance matrix is positive definite.

Value

autocorrelated covariance matrix

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